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On the old Elo system, every 100 points had between 40% and 50% of the people in it from the previous hundred points. Diamond 1 has massive clamping, so I'm not sure of the exact numbers from there, but I'd imagine the spectrum hasn't changed much.

Challenger is capped at 50 players which, according to many players, was a mistake on Riot's part. I haven't investigated it enough to come to my own conclusion on the matter.

Assuming each Division is around 100 Elo, that would leave us with scores between 0 Elo at Bronze V and 2500 Elo at Challenger. These are my guesses as to how many players are in each Division/League based on my past data:

That shows the distribution in the NA server from this season. Basically though about 45% of the players are bronze, and 41% of the players are silver. The remainder is split as 10% gold, 3% platinum, <1% diamond, <1% challenger.

That shows the distribution in the NA server from this season. Basically though about 60% of the players are bronze, and 26% of the players are silver. The remainder is split as 10% gold, 3% platinum, <1% diamond, <1% challenger.

This chart is 3 months old, the one posted in the OP is recent and far more accurate.